Influence of the visco-Pasternak foundation parameters on the buckling behavior of a sandwich functional graded ceramic–metal plate in a hygrothermal environment

This study presents the buckling response of functionally graded (FG) “sandwich plate” on a viscoelastic foundation and exposed to hygrothermal conditions. An accurate solution is developed using higher-order shear deformation theory (HSDT), with only four unknowns being placed to reach the solution. The displacement fields first utilize an indeterminate integral accompanied by a sinusoidal shape function to simulate the transverse shear deformation theory. The foundation’s mathematical model followed the two-Pasternak coefficient model, with one more term being added to represent the damping effect. The sandwich plate is essentially composed of three layers. This study presented three different FG sandwich plate geometric analytical solutions regarding layer orders and composition. The equations of motion were generated according to Hamilton’s principle. Thereafter, the analytical solution was based on Navier’s principle to solve the buckling temperature of a simply supported FG sandwich plate seated on a viscoelastic foundation. This paper shows a parametric study of the effect of the damping coefficient along with the aspect ratio, moisture condition, power-law index, and temperature variation over the buckling temperature of the FG “sandwich plate” on the viscoelastic foundation.